Given $ m \angle CBD = 5x + 13$, $ m \angle ABC = 3x + 33$, and $ m \angle ABD = 70$, find $m\angle ABC$. $B$ $A$ $D$ $C$
Answer: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Substitute in the expressions that were given for each measure: $ {3x + 33} + {5x + 13} = {70}$ Combine like terms: $ 8x + 46 = 70$ Subtract $46$ from both sides: $ 8x = 24$ Divide both sides by $8$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 3({3}) + 33$ Simplify: $ {m\angle ABC = 9 + 33}$ So ${m\angle ABC = 42}$.